# PayPal Holdings Inc (PYPL)

PayPal Holdings, Inc. is an American company operating an online payments system in the majority of countries that support online money transfers, and serves as an electronic alternative to traditional paper methods like checks and money orders. The company operates as a payment processor for online vendors, auction sites, and many other commercial users, for which it charges a fee.

## Stock Price Trends

Stock price trends estimated using linear regression.

#### Key facts

- The primary trend is increasing.
- The growth rate of the primary trend is 23.67% per annum.
- PYPL price at the close of October 4, 2024 was $79.36 and was higher than the top border of the primary price channel by $1.16 (1.49%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 233.72% per annum.
- PYPL price at the close of October 4, 2024 was inside the secondary price channel.

### Linear Regression Model

Model equation:

Y_{i} = α + β × X_{i} + ε_{i}

Top border of price channel:

Exp(Y_{i}) = Exp(a + b × X_{i} + 2 × s)

Bottom border of price channel:

Exp(Y_{i}) = Exp(a + b × X_{i} – 2 × s)

where:

i - observation number

Y_{i} - natural logarithm of PYPL price

X_{i} - time index, 1 day interval

σ - standard deviation of ε_{i}

a - estimator of α

b - estimator of β

s - estimator of σ

Exp() - calculates the exponent of e

### Primary Trend

Start date: September 21, 2023

End date: October 4, 2024

a = 3.1785

b = 0.0006

s = 0.0595

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0006) – 1

= 23.67%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0595) – 1

= 26.87%

#### September 21, 2023 calculations

Top border of price channel:

Exp(Y_{996})

= Exp(a + b × X_{996} + 2 × s)

= Exp(a + b × 1,445 + 2 × s)

= Exp(3.1785 + 0.0006 × 1,445 + 2 × 0.0595)

= Exp(4.1386)

= $62.72

Bottom border of price channel:

Exp(Y_{996})

= Exp(a + b × X_{996} – 2 × s)

= Exp(a + b × 1,445 – 2 × s)

= Exp(3.1785 + 0.0006 × 1,445 – 2 × 0.0595)

= Exp(3.9007)

= $49.44

#### October 4, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,824 + 2 × s)

= Exp(3.1785 + 0.0006 × 1,824 + 2 × 0.0595)

= Exp(4.3592)

= $78.20

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,824 – 2 × s)

= Exp(3.1785 + 0.0006 × 1,824 – 2 × 0.0595)

= Exp(4.1213)

= $61.64

#### Description

- The primary trend is increasing.
- The growth rate of the primary trend is 23.67% per annum.
- PYPL price at the close of October 4, 2024 was $79.36 and was higher than the top border of the primary price channel by $1.16 (1.49%).

### Secondary Trend

Start date: June 26, 2024

End date: October 4, 2024

a = -1.6582

b = 0.0033

s = 0.0339

Annual growth rate:

Exp(365 × b) – 1

= Exp(365 × 0.0033) – 1

= 233.72%

Price channel spread:

Exp(4 × s) – 1

= Exp(4 × 0.0339) – 1

= 14.54%

#### June 26, 2024 calculations

Top border of price channel:

Exp(Y_{1,187})

= Exp(a + b × X_{1,187} + 2 × s)

= Exp(a + b × 1,724 + 2 × s)

= Exp(-1.6582 + 0.0033 × 1,724 + 2 × 0.0339)

= Exp(4.1019)

= $60.45

Bottom border of price channel:

Exp(Y_{1,187})

= Exp(a + b × X_{1,187} – 2 × s)

= Exp(a + b × 1,724 – 2 × s)

= Exp(-1.6582 + 0.0033 × 1,724 – 2 × 0.0339)

= Exp(3.9661)

= $52.78

#### October 4, 2024 calculations

Top border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} + 2 × s)

= Exp(a + b × 1,824 + 2 × s)

= Exp(-1.6582 + 0.0033 × 1,824 + 2 × 0.0339)

= Exp(4.4321)

= $84.10

Bottom border of price channel:

Exp(Y_{1,257})

= Exp(a + b × X_{1,257} – 2 × s)

= Exp(a + b × 1,824 – 2 × s)

= Exp(-1.6582 + 0.0033 × 1,824 – 2 × 0.0339)

= Exp(4.2963)

= $73.43

#### Description

- The secondary trend is increasing.
- The growth rate of the secondary trend is 233.72% per annum.
- PYPL price at the close of October 4, 2024 was inside the secondary price channel.